Finite Group Databasebeta

← #14732251

Subgroups — #14732251

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079557C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3#13078413C211yesmaximal, characteristic, complemented
4#13067795C214yesmaximal, complemented
5#13067732C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067007C211yesmaximal, characteristic, complemented
9C2×D42×C11C211yesmaximal, characteristic
10C23×D4×C11—21no—
11C23×D4×C11—21no—
12D42×C11—22no—
13D42×C11—22no—
14D42×C11—22no—
15D42×C11C2214yes—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C11×#120—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22#10623001C2211yescharacteristic, complemented
23#10622831—22no—
24#10622831—21no—
25#10622828—21no—
26#10622689C2212yescomplemented
27#10622688—22no—
28#10622683C2212yescomplemented
29#10622632C2212yescomplemented
30C4×#4324—22no—
31#10622622—22no—
32#10622621C2212yescomplemented
33#10622621C2212yescomplemented
34#10622620C2212yescomplemented
35#10622584—21no—
36#10622577—21no—
37#10622538C2211yescharacteristic, complemented
38#10622538C2211yescharacteristic, complemented
39#10622537C2211yescharacteristic, complemented
40#10622182C2214yescomplemented
41D4⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C25×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—24no—
47C22×D4×C11—24no—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—48no—
53C22×D4×C11—44no—
54C22×D4×C11—44no—
55C22×D4×C11D411yescharacteristic
56C22×D4×C11D411yescharacteristic
57C22×D4×C11D412yes—
58C23×C4×C11—21no—
59C23×C4×C11—21no—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127D412yes—
63C11×#127C2312yes—
64C11×#121—24no—
65C11×#121—24no—
66C11×#121—24no—
67C11×#121—24no—
68C11×#120—28no—
69C11×#120—28no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11D412yes—
75C4×D4×C11D412yes—
76C4×D4×C11C2312yes—
77C4×D4×C11C2312yes—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4324—22no—
85C2×#4324—24no—
86#66979—21no—
87#66977—21no—
88#66977—21no—
89C2×#4318—21no—
90#66923—21no—
91#66922C2311yescharacteristic, complemented
92#66922C2311yescharacteristic, complemented
93C4×Dic22—21no—
94C4×Dic22—21no—
95#66896—22no—
96#66896—22no—
97#66896—22no—
98#66896—24no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101#66874—22no—
102#66872—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yescomplemented
108C4⋊(C11⋊C8)C2312yescomplemented
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yescomplemented
111#18747—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11—21no—
114C24×C11—28no—
115C24×C11—22no—
116C24×C11—48no—
117C24×C11—48no—
118C24×C11—84no—
119C2×D4×C11—24no—
120C2×D4×C11—28no—
121C2×D4×C11—28no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—44no—
131C2×D4×C11—416no—
132C2×D4×C11—48no—
133C2×D4×C11—48no—
134C2×D4×C11—416no—
135C2×D4×C11—48no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—42no—
140C2×D4×C11—42no—
141C2×D4×C11—82no—
142C2×D4×C11SD1614yescomplemented
143C2×D4×C11C2×D412yes—
144C2×D4×C11C2×D412yes—
145C2×D4×C11C2×D414yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—44no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173C22⋊Dic11—41no—
174#4324—44no—
175#4324—84no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180Dic11⋊C4—41no—
181Dic11⋊C4—41no—
182C4×Dic11—41no—
183#4318—42no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×D42D1111yescharacteristic
188#3208—111no—
189#3101—111no—
190#3077—111no—
191#1639—114no—
192#1629—114no—
193#1545—111no—
194#1486—111no—
195#1478—111no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—44no—
205C23×C11—416no—
206C23×C11—416no—
207C23×C11—44no—
208C23×C11—42no—
209C23×C11—44no—
210C23×C11—88no—
211C23×C11—832no—
212C23×C11#12011yescharacteristic
213D4×C11—24no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—24no—
217D4×C11—44no—
218D4×C11—44no—
219D4×C11—416no—
220D4×C11—416no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—44no—
225D4×C11—82no—
226D4×C11C2×SD1614yes—
227D4×C11AGL(1,ℤ/8)14yes—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—44no—
238C2×C4×C11—44no—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11#12011yescharacteristic
242C2×C4×C11C2×SD1612yes—
243C2×C4×C11AGL(1,ℤ/8)12yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×Dic11—41no—
248C2×Dic11—41no—
249Dic22—42no—
250Dic22—42no—
251C11⋊C8—42no—
252C11⋊C8—42no—
253C11⋊C8—42no—
254C23×D4—21no—
255C23×D4—21no—
256D42—22no—
257D42—22no—
258D42—22no—
259D42C2×D1114yes—
260#533—111no—
261C2×#127C2×D1111yescharacteristic
262C2×#121—21no—
263C2×#121—21no—
264C2×#120—22no—
265C2×C4×D4C2×D1111yescharacteristic
266C2×C4×D4C2×D1111yescharacteristic
267#492—112no—
268#486—112no—
269#483—221no—
270#478—222no—
271#476—112no—
272#476—112no—
273#474—112no—
274#461—112no—
275#460—222no—
276#450—221no—
277#450—222no—
278C4×SD16—222no—
279#431—111no—
280#431—111no—
281#428—221no—
282#423—111no—
283#418—221no—
284#331—114no—
285D4⋊C8—114no—
286D4⋊C8—114no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—48no—
292C22×C11—48no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—44no—
298C22×C11—44no—
299C22×C11—44no—
300C22×C11—88no—
301C22×C11—832no—
302C22×C11#45012yes—
303C22×C11C2×#12011yescharacteristic
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11#45012yes—
310C4×C11C22×SD1611yescharacteristic
311C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C11C2×AGL(1,ℤ/8)12yes—
313Dic11—81no—
314Dic11—81no—
315C25—22no—
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—24no—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—24no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—48no—
325C22×D4—44no—
326C22×D4—44no—
327C22×D4C22⋊D1111yescharacteristic
328C22×D4C22⋊D1111yescharacteristic
329C22×D4C22⋊D1112yes—
330C23×C4—21no—
331C23×C4—21no—
332C2×SD16—222no—
333C2×SD16—224no—
334C2×M16—221no—
335C4⋊Q8—111no—
336C4⋊Q8—111no—
337#127—21no—
338#127—21no—
339#127C22⋊D1112yes—
340#127C22×D1112yes—
341#125—221no—
342C22⋊Q8—221no—
343C22⋊Q8—221no—
344#121—24no—
345#121—24no—
346#121—24no—
347#121—24no—
348#120—28no—
349#120—28no—
350C4×Q8—221no—
351C4×Q8—221no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4C22⋊D1112yes—
357C4×D4C22⋊D1112yes—
358C4×D4C22×D1112yes—
359C4×D4C22×D1112yes—
360#117—221no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22⋊D1111yescharacteristic
363C2×C22⋊C4—22no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C42C22×D1111yescharacteristic
367#107—222no—
368#106—222no—
369#106—222no—
370C4⋊C8—112no—
371C4⋊C8—112no—
372C4⋊C8—221no—
373C4⋊C8—221no—
374#103—222no—
375#102—222no—
376#102—222no—
377#102—222no—
378#102—224no—
379C22⋊C8—221no—
380C22⋊C8—221no—
381C4×C8—112no—
382C4×C8—221no—
383C2×C11—22no—
384C2×C11—44no—
385C2×C11—44no—
386C2×C11—84no—
387C2×C11C2×#45011yescharacteristic
388C2×C11#300311yescharacteristic
389C2×C11#301911yescharacteristic
390C24—21no—
391C24—21no—
392C24—28no—
393C24—22no—
394C24—48no—
395C24—48no—
396C24—84no—
397C2×Q8—221no—
398C2×Q8—221no—
399C2×D4—24no—
400C2×D4—28no—
401C2×D4—28no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—44no—
411C2×D4—416no—
412C2×D4—48no—
413C2×D4—48no—
414C2×D4—416no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—82no—
422C2×D4#432414yescomplemented
423C2×D4C2×C22⋊D1112yes—
424C2×D4C2×C22⋊D1112yes—
425C2×D4C2×C22⋊D1114yes—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—44no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438SD16—444no—
439SD16—884no—
440M16—442no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—221no—
450C4⋊C4—441no—
451C4⋊C4—441no—
452C4⋊C4C2×C22⋊D1112yes—
453C4⋊C4C2×C22⋊D1112yes—
454C22⋊C4—28no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—441no—
460C42—441no—
461C42C2×C22⋊D1111yescharacteristic
462C42C2×C22⋊D1111yescharacteristic
463C42C2×C22⋊D1111yescharacteristic
464C42C23×D1111yescharacteristic
465C11#1874711yescharacteristic, complemented, Sylow
466C23—24no—
467C23—24no—
468C23—22no—
469C23—22no—
470C23—24no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—416no—
476C23—416no—
477C23—44no—
478C23—42no—
479C23—44no—
480C23—88no—
481C23—832no—
482C23#6700611yescharacteristic
483Q8—442no—
484Q8—442no—
485D4—24no—
486D4—22no—
487D4—22no—
488D4—24no—
489D4—44no—
490D4—44no—
491D4—416no—
492D4—416no—
493D4—42no—
494D4—44no—
495D4—42no—
496D4—44no—
497D4—82no—
498D4#6698514yes—
499D4C2×#432414yes—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—44no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4#6698512yes—
514C2×C4C2×#432412yes—
515C2×C4#6700611yescharacteristic
516C2×C4#6700611yescharacteristic
517C2×C4#6700611yescharacteristic
518C2×C4C22×C22⋊D1111yescharacteristic
519C2×C4C22×C22⋊D1111yescharacteristic
520C2×C4C22×C22⋊D1111yescharacteristic
521C8—442no—
522C8—442no—
523C8—442no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—24no—
528C22—48no—
529C22—48no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—44no—
535C22—44no—
536C22—44no—
537C22—88no—
538C22—832no—
539C22#1062283112yes—
540C22C2×#6700611yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—42no—
545C4—42no—
546C4—881no—
547C4—881no—
548C4#1062283112yes—
549C4C2×#6698511yescharacteristic
550C4C2×#6698512yes—
551C4C22×#432411yescharacteristic
552C2—22no—
553C2—44no—
554C2—44no—
555C2—84no—
556C2C2×#1062283111yescharacteristic
557C2#1307784311yescharacteristic
558C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×D42×C11C2
socleC22×C11C2×#120
hypercenterC2×D42D11
hypocenterC11#18747
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13079557C2semidirect
2. #13078624C2semidirect
3. #13078413C2semidirect
4. #13067795C2semidirect
5. #13067732C2semidirect
6. #13067284C2semidirect
7. #13067041C2semidirect
8. #13067007C2semidirect
22. #10623001C22semidirect
26. #10622689C22semidirect
28. #10622683C22semidirect
29. #10622632C22semidirect
32. #10622621C22semidirect
33. #10622621C22semidirect
34. #10622620C22semidirect
37. #10622538C22semidirect
38. #10622538C22semidirect
39. #10622537C22semidirect
40. #10622182C22semidirect
41. D4⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
91. #66922C23semidirect
92. #66922C23semidirect
107. C4⋊(C11⋊C8)C23semidirect
108. C4⋊(C11⋊C8)C23semidirect
110. C4×C11⋊C8C23semidirect
142. C2×D4×C11SD16semidirect
422. C2×D4#4324semidirect
465. C11#18747semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130795572
#130786242
#130784132
#130677952
#130677322
#130672842
#130670412
#130670072
C2×D42×C112
#1874711